fxm3_6 (III)

fxm3_6 dataset

• graph size: 5026 vertex, 44500 edges
• dataset: square matrix of shortest-path-distances of size 5026 * 5026

Environment

library(bigMap)

# source m.list and graph utilities
source('~/bigMap/bdm_xtrs.R')

# range of perplexities given as a fraction of the number of data rows
ppx.list <- c(.01, .05, .10, .20, .30, .40, .50, .60, .70, .80, .90, .95, .99)

Load Data

load('g.RData')
str(g)

## List of 4
##  $ dSet       : chr "fxm3_6"
##  $ data       : int [1:5026, 1:5026] 0 1 1 1 1 1 1 1 1 1 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : NULL
##   .. ..$ : chr [1:5026] "V1" "V2" "V3" "V4" ...
##  $ edges      :'data.frame': 44500 obs. of  2 variables:
##   ..$ V1: int [1:44500] 2 3 4 5 6 7 8 9 10 11 ...
##   ..$ V2: int [1:44500] 1 1 1 1 1 1 1 1 1 1 ...
##  $ is.distance: logi TRUE

Load ptSNE and UMAP results

load('ptSNE_C/glist_C.RData')
g.list <- g.list_C

ptSNE parametric setup

str(g.list[[1]]$ptsne[1:6])

## List of 6
##  $ threads: num 6
##  $ layers : num 3
##  $ rounds : int 4
##  $ boost  : num 1
##  $ theta  : num 0
##  $ alpha  : num 0.5

ptSNE Output

# plot ppx. .01, .05, .10, .20, .30, .50, .50, .70, .90, .95, .99
glist.dev(g.list, method = 'ptsne', path = 'ptSNE_C/', verbose = F)

Quality

Rank-based global/local structure preservation

g.list <- bdm.list.qlty(g.list, g$data, threads = 4, layers = 2, rounds = 2, qm = 'rb', verbose = F)

bdm.list.qlty.plot(g.list, qm = 'rb', y.lim = c(0.8, 1.0))

Kary-neighborhood preservation

g.list_A <- g.list

Previous version (threads = 10, layers = 2, rounds = 1)

load('ptSNE_A/glist_A.RData')

g.list_A <- bdm.list.qlty(g.list_A, g$data, threads = 4, layers = 2, rounds = 2, qm = 'kn', verbose = F)

bdm.list.qlty.plot(g.list_A, qm = 'kn')

Current version (threads = 6, layers = 3, rounds = 4)

g.list_C <- bdm.list.qlty(g.list_C, g$data, threads = 4, layers = 2, rounds = 2, qm = 'kn', verbose = F)

bdm.list.qlty.plot(g.list_C, qm = 'kn')

Running Times

knitr::kable(mlist.rTimes(g.list_C), caption = 'Computation times (s)') %>%
  kable_styling(full_width = F)

Computation times (s)

	50	251	503	1005	1508	2010	2513	3016	3518	4021	4523	4775	4976
ptsne	790	789	791	791	791	790	791	791	791	791	791	787	785

Run on: Intel(R) Xeon(R) CPU E5-2650 v3 2.30GHz, 32Mb cache, 20 cores, 200GB RAM.

Discussion

• UMAP seems to approach better the original visualization of the graph. However, the nearest-neighbours parameter does not seem to have too much impact on the output. All visualizations are quite similar and logAUC and linAUC values are almost invariant with no clear correlation with the nearerst-neighbours parameter.

• ptSNE is much better in terms of linAUC values (overall structure) and clearly shows the effect of perplexity (with linAUC and logAUC showing inverse trends). Also, for low values of perplexity, the logAUC values are similar to those of UMAP, suggesting that the local strucure is similarly detected. But ptSNE seems to go further suggesting two differentiated levels of structure, the first one captured for perplexities up to 0.4 and a second one that starts emerging at perplexity 0.5 and beyond The consistency between the k-ary neihgbourhood preservation plots and the visualization plots supports this idea.

• UMAP is slower (NOTE: umap-learn python module does not fully implement parallelization) and the running times increase with perplexity. For ptSNE, the running times are not affected by perplexity.